Chemistry 103A; Sections 5, 6, 7, 8; Lecture 1; 21 Aug 00

Chemistry 103A; Sections 5, 6, 7, 8; Lecture 21, 11 Oct 00

Recall:

We are using the orbitals originally found in the hydrogen atom to determine the electronic structure of many-electron atoms. We can obtain the electron configuration of an atom using the following rules:

Rule 0: A many electron atom has the same set of orbitals, 1s, 2s, 2p, 3s, 3p, 3d, … etc., that are available in the hydrogen atom and the hydrogen-like ions.

However, the relative energies of the individual orbitals is not the same as in hydrogen. Some of the degeneracy has been lifted.

The p orbitals are still degenerate among themselves, and the d orbitals are degenerate among themselves, and so on, but the 2s and 2p orbitals for, example, are no longer degenerate, and so on.

The order of the energy of the electrons, starting from the lowest energy orbital, the 1s, is

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s, 5g, and so on. (This is more than enough orbitals to take care of the elements that exist.)]

There are two ways to remember this ordering and we will demonstrate both of them in class.

The energy level diagram for a many electron atom (not to scale) looks like:

_8s_

_7p_ _ _

_6d_ _ _ _ _

_5f_ _ _ _ _ _ _

_7s_

_6p_ _ _

_5d_ _ _ _ _

_4f_ _ _ _ _ _ _

_6s_

_5p_ _ _

_4d_ _ _ _ _

_5s_

_4p_ _ _

_3d_ _ _ _ _

_4s_

_3p_ _ _

_3s_

_2p_ _ _

_2s_

_1s_

s p d f g

Rule 1: The "Aufbau" Principle (German for "build up.")

The Aufbau principle says that we fill the lowest energy orbitals first (subject to the other rules to come). Rule 2: The Pauli Exclusion Principle. There can be no more than two electrons in each orbital. If there are two electrons one must be spin up and the other must be spin down. When there are two electrons in an orbital with opposite spins we say that the spins are "paired." Rule 3: Hund's Rule When filling degenerate orbitals keep the spins unpaired as long as possible. Rule 4: Filled shells and subshells are particularly stable, but half filled subshells also have a little extra stability.

By "subshells" we mean all of a group of p orbitals at a particular level (with the same principal quantum number) or all of a group of d orbitals at a particular level.

We will do many examples of predicting electron configurations in class.

Notations for Electron Configurations

Showing the electron configuration for an atom on an orbital energy level diagram, as we have done above, is the most detailed way to display electron configurations. This method of showing the electron configurations is useful in many ways, but this level of detail is not always required.

There are two other ways to display electron configurations which are commonly used.

The next simplest electron configuration display is to show the occupancy of the orbitals by class of orbital. For example, the electron configuration of He would be represented by, 1s², where the superscript 2 indicates that there are two electrons in the He 1s oribtal.

Here are some more examples:

O 1s²2s²2p⁴
Si 1s²2s²2p⁶3s²3p²
Ca 1s²2s²2p⁶3s²3p⁶4s²
Cr 1s²2s²2p⁶3s²3p⁶3d⁵4s¹
Br 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁵
La 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f¹5s²5p⁶6s²

Notice that in this notation we write the orbitals in numerical order rather than in the filling order. There are two reasons for this: One is that it makes it easier to count electrons.

The other reason is that the average distance from the nucleus of the electron in an orbital is proportional to the principal quantum number, n. This means, for example, that an electron in a 6s orbital spends most of its time "outside" of an electron in 4f orbital. Thus writing the electron configuration in numerical order is the same as writing the orbitals in the order of their distance from the nucleus.

A simpler form for writing electron configurations:

As you can see from the above examples, writing electron configurations for elements with high atomic numbers can be tedious. The fact that once you pass a noble gas configuration the configurations of the inner electrons does not change provides a shorthand way of writing configurations.

For example, the shorthand configurations of the elements given above would be,

O [He]2s²2p⁴
Si [Ne]3s²3p²
Ca [Ar]4s²
Cr [Ar]3d⁵4s¹
Br [Ar]3d¹⁰4s²4p⁵
La [Xe]4f¹6s².

This is much simpler than writing the entire configuration out longhand.

The rule is, looking at an electron configuration, you write the symbol of the largest noble gas contained in your configuration in [square brackets]. Then you write the detailed configuration only for the electrons not contained in the noble gas configuration.

Don't misunderstand, the shorthand configuration for La does not mean that there is a xenon atom inside of a lanthanum atom. It simply means that the configuration of the first 54 electrons in La is the same as the Xe configuration.

The Octet Rule

Notice that the outer shell electron configurations of the noble gases larger than He are:

2s²2p⁶, 3s²3p⁶, 4s²4p⁶, 5s²5p⁶, 6s²6p⁶. It was known very early in the history of chemistry that the noble gases are very unreactive. This implies that there is something particularly stable about an outer shell configuration of _s²_p⁶. Since this configuration contains eight electrons it came to be known as an octet.

The Octet rule states that since the eight electron configuration _s²_p⁶ is particularly stable, atoms will tend to gain or lose electrons either by donation or by sharing in order to attain the octet configuration.

This rule provides the basis for understanding the structures of an enormous number of compounds.

The main exceptions to the octet rule occur in atoms with less than five electrons and in the transition metals. For the atoms of H, Li, and Be the nearest noble gas is helium.

Hydrogen forms H⁺ ions (but these exceptions, they really are not bare protons - we will look at these in more detail later).

Hydrogen also forms the hydride ion, H^- which has the helium configuration, 1s².

Helium, of course is a noble gas. There are no known stable compounds of He.

Lithium loses one electron to give the Li⁺ ion which has the helium configuration.

Beryllium loses two electrons to give Be²⁺ ions which also have the helium configuration.

Boron (atomic number 5) is unusual, but it tends not to go to the helium configuration to give ions.

Although the d and f electrons of the transition metals and the lanthanides and actinides complicate matters, their chemistry can still be understood on the basis of their electron configurations

Ions

The octet rule, and the rules for electron configurations, explain virtually all of the monatomic ions.

For example, C, N, O, and F gain electrons to obtain the Ne configuration to give C^4-, N^3-, O^2-, and F^- , respectively.

Na and Mg lose electrons to obtain the Ne configuration, yielding Na⁺ and Mg²⁺ ions respectively.

Al loses three electrons to give A³⁺ ions with the Ne configuration.

K, Ca, Sc and Ti lose electrons to give K⁺, Ca²⁺, Sc³⁺, and Ti⁴⁺ ions respectively.

The transition metals are a little more complex because they have electrons in one of the d subshells.

(Look at the electron configurations of the first ten transition metals.)
Magnetism

There are three main classes of magnetism and they can all be explained by electrons in orbitals. The three main classes of magnetism are, diamagnetism, paramagnetism, and ferromagnetism.

We already know that the electron acts like a tiny magnet. The electron has a north pole and a south pole just like the magnets we are familiar with. We also know that when you try to push two magnets together the north poles repel each other, but the north pole of one magnet will attract the south pole of the other.

An electron alone in an orbital will act like a tiny magnet. If you apply an external magnetic field the electron will try to align itself with the magnetic field.

On the other hand, a pair of electrons in an orbital will not act like a tiny magnet because when the spins are paired the north pole of one electron is pointing the same way as the south pole of the other so that the net north/south effect of electron spin is cancelled.

Paired electrons are diamagnetic. Diamagnetic materials have a very very weak interaction with an external magnetic field. (In fact, they are very slightly repelled by a magnetic field.)

Most common substances are diamagnetic. Wood, cloth, paper, N₂(g), CO₂, water, NaCl, and many others are all diamagnetic. Unpaired electrons are paramagnetic. They are slightly attracted into a magnetic field. This effect is weak enough that you can't tell it is there without sensitive measuring devices. The most common paramagnetic substance that we are familiar with is O₂(g). Ferromagnetism is produced when large groups of atoms (called domains) all align their "atomic magnets" in the same direction.

Fe and Ni are examples of ferromagnetic materials.

In untreated iron the north poles of the domains are pointing in random directions so that the material is not a magnet. Nevertheless, another magnet will strongly attract iron by causing the domains to line up their north/south axes.

You can "magnetize" iron by placing it in a strong magnetic field. The external field will force all the domain north poles to point the same way and this effect will persist even when the external field is turned off.